Police were called to Pistorius's upscale Pretoria home at around 4.00am by neighbours who heard gunshots inside the gated community.
Police spokeswoman Denise Beukes said the 9mm pistol used in the shooting was registered to Pistorius, who authorities have said is the only suspect in the case.
The police said they would oppose any request for bail.
His arrest has rocked South Africa, where he had been considered a hero.
"Obviously we are shocked," his father Henke Pistorius said. "He is with the police and the matter is in the hands of the authorities."
Steenkamp, once an FHM cover girl, was described as "the kindest, sweetest human being; an angel on earth," by Sarit Tomlins of her management agency.
Born in Cape Town, she grew up in Port Elizabeth where she graduated with a degree in law from Nelson Mandela Metropolitan University.
Authorities poured cold water on media reports that she had snuck up on her lover, suggestions that were fuelled by her tweet the day before.
"What do you have up your sleeve for your love tomorrow??? #getexcited #ValentinesDay", she wrote.
South African model Reeva Steenkamp who was shot dead on February 14, 2013 by her South African Olympic sprint star boyfriend Oscar Pistorius. AFP file photo
"We were surprised by allegations that the deceased had been perceived to be a burglar," police spokeswoman Beukes said.
Police said they were talking to neighbours who heard disturbances on Wednesday evening and around the time of the shooting.
There had been previous allegations of domestic disputes at Pistorius's home.
"There were always rumours attracted to Oscar Pistorius, but most of them I just put down to him being a celebrity," said Kyle Wood, a 25-year-old fellow resident of the Silverlakes community.
In 2009 Pistorius spent a night in jail after allegedly assaulting a 19-year-old woman at a party.
A fondness for guns
He has often spoken publicly about his fondness for guns.
Last year he told a newspaper he sleeps with a pistol, machine gun, cricket bat and baseball bat for fear of burglars.
He once took a reporter to a nearby shooting range with his 9mm handgun after learning that the journalist had never fired a shot.
There are an estimated 1.5 million gun owners in South Africa, where crime remains a major problem.
Many residents keep weapons at home and equip their houses with electric fences and panic buttons that summon heavily armed guards within minutes.
In November, Pistorius tweeted about arriving home and hearing the washing machine on "and thinking it's an intruder to go into full combat recon mode into the pantry! waa."
His right to have a gun was called into question by South Africa's anti-firearms lobby.
South Africa's Oscar Pistorius wins gold in the men's 400-meter T44 final at the 2012 Paralympics, in London. AP file photo
To be licensed as a gun owner, Pistorius would have had to seek a competency certificate that requires knowledge of gun laws and interviews with his neighbours to rule out issues around addiction, mental illness or violence.
"With Oscar's case it is quite interesting because it does appear that there was a history of abuse and possible alcohol misuse," said Claire Taylor of Gun Free South Africa.
Pistorius was also known as an adrenaline junkie, with a love of speed reflected in a passion for motorbikes. Four years ago he crashed his boat in a river south of Johannesburg, breaking two ribs, an eye socket and his jaw.
Empty alcohol bottles were found in the boat, but his blood alcohol content was not tested.
Until now his problems off the track had been eclipsed by his success on it.
The Johannesburg-born athlete won gold in the 4x100m relay and the 400m individual at the Paralympic Games in London. He was triple gold medallist in the Beijing games in 2008.
He was named by Time Magazine last year as one of the world's 100 most influential people.
He had both legs amputated below the knee when he was 11-months-old after being born without lower leg bones. But he played sports unhindered while growing up, switching to running after fracturing a knee playing rugby.
At high school, he was so good that his personal fitness coach said she was unaware for six months that he ran on prosthetic legs.
Already a South African pay television channel has canned a campaign featuring the runner.
There was no immediate comment from global sports giant Nike on its sponsorship of Pistorius, who it featured in an advert showing the runner setting off from the starting blocks with the line "I am the bullet in the chamber".